Question

select the correct answer.
which equation best models the set of data in this table?
a. $y = 33sqrt{x}+32.7$
b. $y = 33sqrt{x}-32.7$
c. $y = 33x + 32.7$
d. $y = 33x - 32.7$

Explanation:

Step1: Substitute \(x = 0\) into each equation

• For option A: \(y=33\sqrt{0}+32.7=32.7\approx32\)
• For option B: \(y = 33\sqrt{0}-32.7=- 32.7\)
• For option C: \(y=33\times0 + 32.7=32.7\approx32\)
• For option D: \(y=33\times0-32.7=-32.7\)

Step2: Substitute \(x = 1\) into the remaining possible equations (A and C)

• For option A: \(y=33\sqrt{1}+32.7=33 + 32.7=65.7\approx67\)
• For option C: \(y=33\times1+32.7=33 + 32.7=65.7

eq67\) (Since when \(x = 1\), the value from option C is not close enough to the table value of \(y = 67\) compared to option A)

Answer:

A. \(y = 33\sqrt{x}+32.7\)